4 Sketched Proof of the Correctness

We emphasize here that the weak learning algorithm A does not know the distribution D. It only sees samples from D. The time and sampling complexity of A usually depends on δ and γ. The definition of weak learner is different from the normal but strong version of PAC learning in terms of the error guarantee: the strong version requires that for any ε > 0, the error PrD[f(x) 6= c(x)] can be made as small as ε. (Recall that we have learned from the previous lecture on how to obtain a weak leaner for monotone functions, but only when the distribution is uniform. If that weak leaner worked for all distributions (i.e., is distribution-free), it would imply that monotone functions can be PAC learned in the strong sense, contradicting to the impossibility result.)